To determine the volume of a gas at standard temperature and pressure (STP), we need to use the ideal gas law, which states:
PV = nRT
Where: P = Pressure of the gas V = Volume of the gas n = Number of moles of the gas R = Ideal gas constant T = Temperature of the gas
At STP, the temperature is 0°C or 273.15K, and the pressure is 101.3 kPa.
First, we need to calculate the number of moles (n) of the gas at the given conditions using the ideal gas law:
PV = nRT
n = PV / RT
Given: P = 99.3 kPa V = 480 mL = 480 cm³ T = 40°C = 40 + 273.15 = 313.15K
Now we can calculate n:
n = (99.3 kPa * 480 cm³) / (8.314 J/(mol·K) * 313.15K)
n ≈ 19.70 millimoles (mmol) or 0.0197 moles
Now, to find the volume at STP, we can rearrange the ideal gas law equation:
V1 / T1 = V2 / T2
Where: V1 = Volume at the given conditions T1 = Temperature at the given conditions V2 = Volume at STP T2 = Temperature at STP (273.15K)
Rearranging the equation, we get:
V2 = (V1 * T2) / T1
Plugging in the values:
V2 = (480 cm³ * 273.15K) / 313.15K
V2 ≈ 418.35 cm³ or 418.35 mL
Therefore, the volume the gas occupies at STP is approximately 418.35 mL.